MAGIC115: Lusztig’s conjecture

Course details

A specialist MAGIC course

Semester

Spring 2025
Monday, January 27th to Friday, April 4th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
40

Timetable

Tuesdays
12:05 - 12:55 (UK)

Course forum

Visit the https://v2.maths-magic.ac.uk/forums/magic115-lusztigs-conjecture

Description

The course covers the basics of Hecke categories and their associated p-Kazhdan–Lusztig polynomials. Over the past decade, Hecke categories have arisen as some of the most important structures in representation theory and have been used to resolve some of the field’s most famous conjectures. The purpose of this course is to give a hands-on introduction to working with Hecke categories and a thorough grounding in their basic structures.

Prerequisites

Familiarity with abstract algebra and complex representation theory or character theory of symmetric groups is desirable. The following are no strict pre-requisites, but familiarity with the ideas discussed in the following books would not hurt:

Chapter 1-11 of James-Liebeck’s book “Representations and characters of groups”. 
Chapter 2 of Mathas' book "Iwahori–Hecke algebras and Schur algebras of the symmetric group"
Chapters 5-6 of Bowman's book "Diagrammatic Algebra" (preprint available in the "files" section of this course)

Syllabus

Topics covered:
(1)   Cellular algebras
(2)   Representations of Schur algebras and symmetric groups
(3)   Kazhdan-Lusztig polynomials via Temperley—Lieb combinatorics 
(4)   General Kazhdan-Lusztig polynomials
(5)   The Hecke category of maximal parabolics of symmetric groups
(6)   The Hecke category of the affine symmetric group
(7)   Intersection forms 
(8)   Torsion explosion in the Hecke category 

Lecturer

  • CB

    Chris Bowman-Scargill

    University
    University of York

Bibliography

No bibliography has been specified for this course.

Assessment

The assessment for this course will be released on Tuesday 22nd April 2025 at 00:00 and is due in before Monday 5th May 2025 at 11:00.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Please note that you are not registered for assessment on this course.

Files

Only current consortium members and subscribers have access to these files.

Please log in to view course materials.

Lectures

Please log in to view lecture recordings.